Statistics and Probability Answers

An economics consulting firm has created a model to predict recessions. The model predicts a recession with a probability of 80% when a recession is indeed coming and with a probability of 10% when no recession is coming. The unconditional probability of falling into a recession is 20%. If the model predicts a recession, what is the probability that a recession will indeed come?

Question 4 [16 Marks]

Research has shown that about 2% of all products produced by BVH Company are defective. A quality

inspector has just sampled 300 products from this company. Using the Poisson distribution, what is the

probability that:

(a) exactly 12 of them are defective? [4]

(b) at least 8 of them are defective?

Question 3 [15 Marks]

3.1 Answer questions a, b and c below:

a) If we roll a fair die and toss a coin, the total number of possible outcomes is: [2]

b) If we roll a fair 4-sided die 3 times, the total number of possible outcomes is: [2]

c) Teams M and N play in a basketball tournament. The team that first wins three games wins the

tournament. Draw the tree diagram that present all possible course of the tournament. [6]

c

3.2 Find 𝑥 if 2𝑃(𝑥,2) + 50 = 𝑃(2𝑥,2)

Question 2 [4 Marks]

Consider the following subsets of 𝑆 = {1, 2, 3, … ,8,9}:

(𝑖) [{1,3,5},{2,4,6,8},{5,7,9}]

(𝑖𝑖) [{1,3,5},{2,4,6,8},{7,9}]

Does 𝑖 and 𝑖𝑖 form a partition on sample space �

Suppose that in a certain Senior High School the average height of male students is 155.9 cm with standard deviation of 20.4 cm. If you choose 40 students what is the probability that their height is above 155 cm?

A pinball machine has five holes of varying sizes in which the ball may land. The payoff for the

ball landing in a given hole indicates that the probabilities of success for various holes should be

0.28, 0.24, 0.19, 0.15 and 0.14.

A contestant plays the game 42 times and obtains the following frequencies: 15, 10, 7, 6 and 4. Test

at a 5% level of significance whether the probabilities corresponding to the payoffs are correct.

Suppose X and Y are random variables with P(X = 1) = P(X = −1) = 1/2 ; P(Y = 1) = P(Y = −1) = 1/2 . Let c = P(X = 1 and Y = 1) (a) Determine the joint distribution of X and Y, Cov(X,Y), and r(X,Y). (b) For what value(s) of c are X and Y independent? For what value(s) of c are X and Y 100% correlated?

A population consists of the five numbers: 1, 3, 5, 7, and 9.

Consider samples of size 3 that can be drawn from this population

2 points for every Sample and 1 point for the corresponding Mean of that Sample

A population consists of the five numbers: 1, 3, 5, 7, and 9.

Consider samples of size 3 that can be drawn from this population

2 points for every Sample and 1 point for the corresponding Mean of that Sample

A fastfood chain's softdrink machine is calibrated so that it disperses an average of 225 milliliters per cup. The amount of drink is normally distributed with a standard deviation equal to 15 milliliters.